Question

express in simplest radical form.

$-9\sqrt{108} + \sqrt{27}$

answer
attempt 1 out of 2

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Explanation:

Step1: Simplify \(\sqrt{108}\)

Factor 108: \(108 = 36\times3\), so \(\sqrt{108}=\sqrt{36\times3}=\sqrt{36}\times\sqrt{3}=6\sqrt{3}\)

Step2: Simplify \(\sqrt{27}\)

Factor 27: \(27 = 9\times3\), so \(\sqrt{27}=\sqrt{9\times3}=\sqrt{9}\times\sqrt{3}=3\sqrt{3}\)

Step3: Substitute back into the original expression

\(-9\sqrt{108}+\sqrt{27}=-9\times6\sqrt{3}+3\sqrt{3}=-54\sqrt{3}+3\sqrt{3}\)

Step4: Combine like terms

\(-54\sqrt{3}+3\sqrt{3}=(-54 + 3)\sqrt{3}=-51\sqrt{3}\)

Answer:

\(-51\sqrt{3}\)